Teaching

Spring 2015

This course is an introduction to computational geometry and its applications focusing on algorithms and data structures. It will cover various techniques needed in designing and analyzing efficient algorithms for computational problems in discrete geometry including convex hulls, triangulations, geometric intersections, Voronoi diagrams and Delaunay triangulations, arrangements of lines and hyperplanes, range searching. Computational geometry is well related to a variety of application domains in which geometric algorithms play a fundamental role, such as pattern recognition, image processing, computer graphics, robotics, geographic information systems (GIS), computer-aided design (CAD), information retrieval, computational science, and many others. The course will cover general algorithmic techniques, such as plane sweep, divide and conquer, incremental construction, randomisation, and approximation, through their application to basic geometric problems.

Fall 2014

This course will introduce the student to logic and to the idea that one can use logical techniques to "prove" mathematical statements. To some extent most students have already "proved" mathematical statements by mechanically manipulating algebraic equations in order to arrive at an answer. For example, proving that a quadratic equation has particular roots. But students are probably unaware that logic is at work underneath the manipulations. In this course, logic and its descriptive power will be explored, and then used to construct more complicated proofs about abstract objects like sets, relations and functions. The student will learn how to structure and execute a logically correct mathematical proof and to analyze proofs written by others.

Spring 2014

Geometric Algorithms

Academic year 2013/2014 - Spring semester

Professor: Evanthia Papadopoulou

Assistant: Sumedha Gupta

Fall 2013

Discrete Mathematics I

Academic year 2013/2014 - Fall semester

Professor: Evanthia Papadopoulou

Assistant: Maksym Zavershynskyi

Assistant: Sandeep Kumar Dey

Fall 2012

Discrete Mathematics 1

Academic year 2012/2013 - Fall semester

Professor: Evanthia Papadopoulou

Assistant: Maksym Zavershynskyi

Assistant: Sandeep Kumar Dey

Topics in Algorithms

Academic year 2012/2013 - Fall semester

Professor: Evanthia Papadopoulou

Instructor: Panagiotis Cheilaris

Assistant: Elena Khramtcova

The course covered a variety of topics such as disjoint-sets data structures and the union-find algorithm, graphs and graph algorithms (for example, shortest paths computation), interval trees, randomized algorithms (Monte Carlo and Las Vegas algorithms) and their probabilistic analysis, intractability and NP completeness, how to deal with intractability, approximation algorithms.